Question: $88$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $100$ less than $3$ times the number of away team fans. How many home team and away team fans attended the game?
Explanation: Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 88}$ ${x = 3y-100}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${3y-100}$ for $x$ in the first equation. ${(3y-100)}{+ y = 88}$ Simplify and solve for $y$ $ 3y-100 + y = 88 $ $ 4y-100 = 88 $ $ 4y = 188 $ $ y = \dfrac{188}{4} $ ${y = 47}$ Now that you know ${y = 47}$ , plug it back into ${x = 3y-100}$ to find $x$ ${x = 3}{(47)}{ - 100}$ $x = 141 - 100$ ${x = 41}$ You can also plug ${y = 47}$ into ${x+y = 88}$ and get the same answer for $x$ ${x + }{(47)}{= 88}$ ${x = 41}$ There were $41$ home team fans and $47$ away team fans.